Let \( \mathbf {X}= ( X^i)_{i\in \mathbb {Z} }\)  be a solution to ISDE (REF )
with \( \beta = 2 \)  defined on a filtered space \( (\Omega , {F}, P , \lbrace  {F}_t \rbrace  )\) 
such that \( \mathbf {X}_0 \stackrel{\mathrm {law}}{=}\mu \circ {\mathfrak {l} }^{-1}\) .
Then it is known [1]} that
\(&P(\mathfrak {u} _{\mathrm {path}}(\mathbf {X}) \in \cdot | \mathbf {X}= \mathbf {x}) = \mathsf {P}_{\mathfrak {x}}\quad \text{ for $ \mathbf {x}= \mathfrak {l} (\mathfrak {x}) $}.\) 
